Large Solutions for Fractional Laplacian on Infinite Cylindrical Domains
Abstract
We investigate large solutions of linear and semi-linear equations involving the fractional Laplacian on domains that are becoming unbounded in some, but not all, directions. Solutions that blow up on the boundary of a domain are commonly called large solutions. For local operators, such behaviour arises only in the presence of lower-order nonlinear terms. However, for nonlocal operators, the existence of such solutions is more subtle. In contrast to the local case, the nonlocal nature of the operator gives rise to different boundary blow-up phenomena even in the case of linear equations. In this article, we study the existence and qualitative behaviour of boundary blow-up solutions to fractional linear and semi-linear equations on finite cylindrical domains and employ these properties to construct large solutions on infinite cylinders.
Related
- Symmetry of solutions to nonlocal Neumann problems with the fractional Laplacian in half spaces
- Boundary Harnack inequalities for the fractional p-Laplacian in Reifenberg flat domains
- The direct moving plane method for weak solutions of the fractional p-Laplacian
- Hölder regularity of solutions to parabolic equations associated with fractional p-Laplacian type operators
- Neumann Schrödinger Estimates in Cylindrical Domains
BibTeX
@misc{chowdhury2026large,
title = {{Large Solutions for Fractional Laplacian on Infinite Cylindrical Domains}},
author = {Indranil Chowdhury and N N Dattatreya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.25906},
eprint = {2607.25906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25906},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large Solutions for Fractional Laplacian on Infinite Cylindrical Domains
AU - Indranil Chowdhury
AU - N N Dattatreya
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.25906
UR - https://arxiv.org/abs/2607.25906
AB - We investigate large solutions of linear and semi-linear equations involving the fractional Laplacian on domains that are becoming unbounded in some, but not all, directions. Solutions that blow up on the boundary of a domain are commonly called large solutions. For local operators, such behaviour arises only in the presence of lower-order nonlinear terms. However, for nonlocal operators, the existence of such solutions is more subtle. In contrast to the local case, the nonlocal nature of the operator gives rise to different boundary blow-up phenomena even in the case of linear equations. In this article, we study the existence and qualitative behaviour of boundary blow-up solutions to fractional linear and semi-linear equations on finite cylindrical domains and employ these properties to construct large solutions on infinite cylinders.
ER -